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The doctrinal paradox, the discursive dilemma, and logical aggregation theory

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  • Philippe Mongin

Abstract

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
  • Handle: RePEc:kap:theord:v:73:y:2012:i:3:p:315-355
    DOI: 10.1007/s11238-012-9310-y
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    2. Crès, Hervé & Tvede, Mich, 2022. "Aggregation of opinions in networks of individuals and collectives," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. Klaus Nehring & Marcus Pivato, 2022. "The median rule in judgement aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1051-1100, June.
    4. Zoi Terzopoulou & Ulle Endriss, 2020. "Neutrality and relative acceptability in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 25-49, June.
    5. MANIQUET, François & MONGIN, Philippe, 2014. "Judgment aggregation theory can entail new social choice results," LIDAM Discussion Papers CORE 2014054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    7. Jean Baccelli & Marcus Pivato, 2021. "Philippe Mongin (1950–2020)," Theory and Decision, Springer, vol. 90(1), pages 1-9, February.
    8. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    9. Aureli Alabert & Mercè Farré & Rubén Montes, 2023. "Optimal Decision Rules for the Discursive Dilemma," Group Decision and Negotiation, Springer, vol. 32(4), pages 889-923, August.
    10. Herzberg, Frederik, 2017. "Respect for experts vs. respect for unanimity: The liberal paradox in probabilistic opinion pooling," Economics Letters, Elsevier, vol. 151(C), pages 44-47.
    11. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.

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    More about this item

    Keywords

    Judgment aggregation; Logical aggregation; Doctrinal paradox; Discursive dilemma; General logic; Premiss-based vs. conclusion-based approach; Social choice theory; Impossibility theorems; D 70; D 71; D 79;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other

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